##############ECHO OF PROBLEM#################
##############temp/sinh_sqrtpostode.ode#################
diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ;
!
/* BEGIN FIRST INPUT BLOCK */
Digits=32;
max_terms=30;
!
/* END FIRST INPUT BLOCK */
/* BEGIN SECOND INPUT BLOCK */
x_start=2.0;
x_end=3.0;
array_y_init[0 + 1] = exact_soln_y(x_start);
glob_look_poles=true;
glob_max_iter=1000000;
glob_max_h=0.00001;
/* END SECOND INPUT BLOCK */
/* BEGIN OVERRIDE BLOCK */
glob_desired_digits_correct=10;
glob_display_interval=0.01;
glob_look_poles=true;
glob_max_iter=1000000000;
glob_max_minutes=30.0;
glob_subiter_method=3;
/* END OVERRIDE BLOCK */
!
/* BEGIN USER DEF BLOCK */
double exact_soln_y (double x) {
return(20.0 * sqrt(0.1 * x + 0.2) * cosh( sqrt(0.1 * x + 0.2)) - 20.0 * sinh( sqrt(0.1 * x + 0.2)));
}
/* END USER DEF BLOCK */
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
estimated_h = 1e-06
estimated_answer = 1
desired_abs_gbl_error = 1e-10
range = 1
estimated_steps = 1000000
step_error = 1e-16
est_needed_step_err = 1e-16
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.211685631110643e-176
estimated_step_error = 5.211685631110643e-176
best_h = 2e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.497502625623425e-168
estimated_step_error = 3.497502625623425e-168
best_h = 4e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.34713374802993e-160
estimated_step_error = 2.34713374802993e-160
best_h = 8e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.575134080294016e-152
estimated_step_error = 1.575134080294016e-152
best_h = 1.6e-05
opt_iter = 5
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.057053628684534e-144
estimated_step_error = 1.057053628684534e-144
best_h = 1e-05
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 1.754980921980319
y[1] (numeric) = 1.754980921980319
absolute error = 0
relative error = 0 %
Correct digits = 16
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.999
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 6.943
Order of pole (six term test) = -0.7206
TOP MAIN SOLVE Loop
x[1] = 2.010000000000066
y[1] (analytic) = 1.761740396662304
y[1] (numeric) = 1.761740391894056
absolute error = 4.768248018649501e-09
relative error = 2.706555419676565e-07 %
Correct digits = 9
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.009
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 6.961
Order of pole (six term test) = -0.7206
TOP MAIN SOLVE Loop
x[1] = 2.020000000000131
y[1] (analytic) = 1.768509403906323
y[1] (numeric) = 1.768509394373666
absolute error = 9.532657330169059e-09
relative error = 5.390221453792166e-07 %
Correct digits = 9
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.019
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 6.979
Order of pole (six term test) = -0.7205
TOP MAIN SOLVE Loop
x[1] = 2.030000000000197
y[1] (analytic) = 1.775287936060764
y[1] (numeric) = 1.775287921767514
absolute error = 1.429324947288535e-08
relative error = 8.05122886409122e-07 %
Correct digits = 9
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.029
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 6.996
Order of pole (six term test) = -0.7204
TOP MAIN SOLVE Loop
x[1] = 2.040000000000262
y[1] (analytic) = 1.782075985508431
y[1] (numeric) = 1.78207596645838
absolute error = 1.905005087010636e-08
relative error = 1.068980841727202e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.039
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 7.014
Order of pole (six term test) = -0.7203
TOP MAIN SOLVE Loop
x[1] = 2.050000000000328
y[1] (analytic) = 1.78887354466629
y[1] (numeric) = 1.788873520863231
absolute error = 2.380305819116302e-08
relative error = 1.330617150783759e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.049
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 7.032
Order of pole (six term test) = -0.7203
TOP MAIN SOLVE Loop
x[1] = 2.060000000000393
y[1] (analytic) = 1.795680605985325
y[1] (numeric) = 1.795680577433017
absolute error = 2.855230785137053e-08
relative error = 1.590054921582411e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.059
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 7.049
Order of pole (six term test) = -0.7202
TOP MAIN SOLVE Loop
x[1] = 2.070000000000459
y[1] (analytic) = 1.802497161950244
y[1] (numeric) = 1.80249712865244
absolute error = 3.329780362548718e-08
relative error = 1.847315176322387e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.069
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 7.067
Order of pole (six term test) = -0.7201
TOP MAIN SOLVE Loop
x[1] = 2.080000000000524
y[1] (analytic) = 1.809323205079338
y[1] (numeric) = 1.809323167039768
absolute error = 3.803956905024108e-08
relative error = 2.10241978566638e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.079
Order of pole (three term test) = 1.507
Radius of convergence (six term test) for eq 1 = 7.085
Order of pole (six term test) = -0.7201
TOP MAIN SOLVE Loop
x[1] = 2.09000000000059
y[1] (analytic) = 1.816158727924215
y[1] (numeric) = 1.816158685146597
absolute error = 4.277761744830855e-08
relative error = 2.355389801044613e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.089
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.102
Order of pole (six term test) = -0.72
TOP MAIN SOLVE Loop
x[1] = 2.100000000000655
y[1] (analytic) = 1.823003723069625
y[1] (numeric) = 1.823003675557661
absolute error = 4.751196436281191e-08
relative error = 2.606246150875102e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.099
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.12
Order of pole (six term test) = -0.7199
TOP MAIN SOLVE Loop
x[1] = 2.110000000000721
y[1] (analytic) = 1.829858183133245
y[1] (numeric) = 1.829858130890612
absolute error = 5.224263310843469e-08
relative error = 2.855009945031927e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.109
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.138
Order of pole (six term test) = -0.7199
TOP MAIN SOLVE Loop
x[1] = 2.120000000000786
y[1] (analytic) = 1.836722100765465
y[1] (numeric) = 1.836722043795833
absolute error = 5.696963234491648e-08
relative error = 3.101701249262152e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.119
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.156
Order of pole (six term test) = -0.7198
TOP MAIN SOLVE Loop
x[1] = 2.130000000000852
y[1] (analytic) = 1.843595468649193
y[1] (numeric) = 1.84359540695621
absolute error = 6.169298250036093e-08
relative error = 3.346340536710233e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.129
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.173
Order of pole (six term test) = -0.7197
TOP MAIN SOLVE Loop
x[1] = 2.140000000000917
y[1] (analytic) = 1.850478279499656
y[1] (numeric) = 1.850478213086959
absolute error = 6.641269711948894e-08
relative error = 3.58894767127156e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.139
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.191
Order of pole (six term test) = -0.7197
TOP MAIN SOLVE Loop
x[1] = 2.150000000000983
y[1] (analytic) = 1.857370526064196
y[1] (numeric) = 1.8573704549354
absolute error = 7.112879596427035e-08
relative error = 3.829542623086285e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.149
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.209
Order of pole (six term test) = -0.7196
TOP MAIN SOLVE Loop
x[1] = 2.160000000001048
y[1] (analytic) = 1.864272201122079
y[1] (numeric) = 1.864272125280783
absolute error = 7.584129613213975e-08
relative error = 4.068144989046769e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.159
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.226
Order of pole (six term test) = -0.7195
TOP MAIN SOLVE Loop
x[1] = 2.170000000001114
y[1] (analytic) = 1.871183297484269
y[1] (numeric) = 1.871183216934067
absolute error = 8.05502013978554e-08
relative error = 4.30477342899287e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.169
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.244
Order of pole (six term test) = -0.7194
TOP MAIN SOLVE Loop
x[1] = 2.180000000001179
y[1] (analytic) = 1.878103807993289
y[1] (numeric) = 1.878103722737749
absolute error = 8.525554084926057e-08
relative error = 4.539447739065826e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.179
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.262
Order of pole (six term test) = -0.7194
TOP MAIN SOLVE Loop
x[1] = 2.190000000001245
y[1] (analytic) = 1.885033725522979
y[1] (numeric) = 1.885033635565652
absolute error = 8.995732669880852e-08
relative error = 4.77218659172005e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.189
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.279
Order of pole (six term test) = -0.7193
TOP MAIN SOLVE Loop
x[1] = 2.20000000000131
y[1] (analytic) = 1.89197304297832
y[1] (numeric) = 1.891972948322749
absolute error = 9.46555704928187e-08
relative error = 5.003008411991596e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.199
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.297
Order of pole (six term test) = -0.7192
TOP MAIN SOLVE Loop
x[1] = 2.210000000001376
y[1] (analytic) = 1.898921753295248
y[1] (numeric) = 1.898921653944964
absolute error = 9.935028355556597e-08
relative error = 5.23193140439625e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.209
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.315
Order of pole (six term test) = -0.7192
TOP MAIN SOLVE Loop
x[1] = 2.220000000001441
y[1] (analytic) = 1.905879849440472
y[1] (numeric) = 1.905879745398979
absolute error = 1.040414931985367e-07
relative error = 5.458974406444415e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.219
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.333
Order of pole (six term test) = -0.7191
TOP MAIN SOLVE Loop
x[1] = 2.230000000001507
y[1] (analytic) = 1.912847324411274
y[1] (numeric) = 1.912847215682062
absolute error = 1.087292123003181e-07
relative error = 5.684155285826702e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.229
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.35
Order of pole (six term test) = -0.719
TOP MAIN SOLVE Loop
x[1] = 2.240000000001572
y[1] (analytic) = 1.919824171235319
y[1] (numeric) = 1.919824057821872
absolute error = 1.134134473002035e-07
relative error = 5.90749137340151e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.239
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.368
Order of pole (six term test) = -0.719
TOP MAIN SOLVE Loop
x[1] = 2.250000000001638
y[1] (analytic) = 1.926810382970503
y[1] (numeric) = 1.926810264876281
absolute error = 1.18094222401055e-07
relative error = 6.129000728083731e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.249
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.386
Order of pole (six term test) = -0.7189
TOP MAIN SOLVE Loop
x[1] = 2.260000000001703
y[1] (analytic) = 1.933805952704731
y[1] (numeric) = 1.933805829933185
absolute error = 1.227715460405676e-07
relative error = 6.348700388932632e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.259
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.404
Order of pole (six term test) = -0.7188
TOP MAIN SOLVE Loop
x[1] = 2.270000000001769
y[1] (analytic) = 1.940810873555767
y[1] (numeric) = 1.940810746110334
absolute error = 1.274454328736851e-07
relative error = 6.566607525244944e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.269
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.421
Order of pole (six term test) = -0.7188
TOP MAIN SOLVE Loop
x[1] = 2.280000000001834
y[1] (analytic) = 1.947825138671041
y[1] (numeric) = 1.947825006555136
absolute error = 1.321159046607789e-07
relative error = 6.782739478910247e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.279
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.439
Order of pole (six term test) = -0.7187
TOP MAIN SOLVE Loop
x[1] = 2.2900000000019
y[1] (analytic) = 1.954848741227472
y[1] (numeric) = 1.9548486044445
absolute error = 1.367829725040792e-07
relative error = 6.997112851718215e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.289
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.457
Order of pole (six term test) = -0.7186
TOP MAIN SOLVE Loop
x[1] = 2.300000000001965
y[1] (analytic) = 1.961881674431302
y[1] (numeric) = 1.961881532984648
absolute error = 1.41446654389199e-07
relative error = 7.209744411838736e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.299
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.474
Order of pole (six term test) = -0.7186
TOP MAIN SOLVE Loop
x[1] = 2.310000000002031
y[1] (analytic) = 1.968923931517898
y[1] (numeric) = 1.968923785410939
absolute error = 1.461069587538333e-07
relative error = 7.420650255451738e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.309
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.492
Order of pole (six term test) = -0.7185
TOP MAIN SOLVE Loop
x[1] = 2.320000000002096
y[1] (analytic) = 1.975975505751613
y[1] (numeric) = 1.97597535498771
absolute error = 1.507639029174612e-07
relative error = 7.629846750560518e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.319
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.51
Order of pole (six term test) = -0.7184
TOP MAIN SOLVE Loop
x[1] = 2.330000000002162
y[1] (analytic) = 1.983036390425585
y[1] (numeric) = 1.98303623500809
absolute error = 1.554174953177778e-07
relative error = 7.837349635546689e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.329
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.528
Order of pole (six term test) = -0.7183
TOP MAIN SOLVE Loop
x[1] = 2.340000000002227
y[1] (analytic) = 1.990106578861583
y[1] (numeric) = 1.990106418793822
absolute error = 1.600677617119572e-07
relative error = 8.043175346092373e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.339
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.545
Order of pole (six term test) = -0.7183
TOP MAIN SOLVE Loop
x[1] = 2.350000000002293
y[1] (analytic) = 1.997186064409831
y[1] (numeric) = 1.997185899695124
absolute error = 1.647147076511146e-07
relative error = 8.247339123097067e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.349
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.563
Order of pole (six term test) = -0.7182
TOP MAIN SOLVE Loop
x[1] = 2.360000000002358
y[1] (analytic) = 2.004274840448847
y[1] (numeric) = 2.004274671090502
absolute error = 1.693583446815694e-07
relative error = 8.44985634024336e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.359
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.581
Order of pole (six term test) = -0.7181
TOP MAIN SOLVE Loop
x[1] = 2.370000000002424
y[1] (analytic) = 2.01137290038527
y[1] (numeric) = 2.011372726386567
absolute error = 1.739987034454771e-07
relative error = 8.650743152209536e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.369
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.599
Order of pole (six term test) = -0.7181
TOP MAIN SOLVE Loop
x[1] = 2.380000000002489
y[1] (analytic) = 2.018480237653685
y[1] (numeric) = 2.01848005901791
absolute error = 1.786357759492319e-07
relative error = 8.850013619993674e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.379
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.616
Order of pole (six term test) = -0.718
TOP MAIN SOLVE Loop
x[1] = 2.390000000002555
y[1] (analytic) = 2.025596845716505
y[1] (numeric) = 2.025596662446904
absolute error = 1.832696012726842e-07
relative error = 9.047683978193455e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.389
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.634
Order of pole (six term test) = -0.7179
TOP MAIN SOLVE Loop
x[1] = 2.40000000000262
y[1] (analytic) = 2.032722718063738
y[1] (numeric) = 2.032722530163574
absolute error = 1.879001638727118e-07
relative error = 9.243767593235509e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.399
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.652
Order of pole (six term test) = -0.7179
TOP MAIN SOLVE Loop
x[1] = 2.410000000002686
y[1] (analytic) = 2.03985784821289
y[1] (numeric) = 2.039857655685395
absolute error = 1.925274943914701e-07
relative error = 9.438279954661673e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.409
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.669
Order of pole (six term test) = -0.7178
TOP MAIN SOLVE Loop
x[1] = 2.420000000002752
y[1] (analytic) = 2.047002229708774
y[1] (numeric) = 2.047002032557164
absolute error = 1.971516101484383e-07
relative error = 9.631235730333668e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.419
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.687
Order of pole (six term test) = -0.7177
TOP MAIN SOLVE Loop
x[1] = 2.430000000002817
y[1] (analytic) = 2.054155856123353
y[1] (numeric) = 2.054155654350835
absolute error = 2.017725182490437e-07
relative error = 9.822648931314936e-06 %
Correct digits = 8
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.429
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.705
Order of pole (six term test) = -0.7177
TOP MAIN SOLVE Loop
x[1] = 2.440000000002883
y[1] (analytic) = 2.061318721055592
y[1] (numeric) = 2.061318514665363
absolute error = 2.063902289073383e-07
relative error = 1.00125335688819e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.439
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.723
Order of pole (six term test) = -0.7176
TOP MAIN SOLVE Loop
x[1] = 2.450000000002948
y[1] (analytic) = 2.068490818131302
y[1] (numeric) = 2.068490607126545
absolute error = 2.110047567782658e-07
relative error = 1.020090371824275e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.449
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.74
Order of pole (six term test) = -0.7175
TOP MAIN SOLVE Loop
x[1] = 2.460000000003014
y[1] (analytic) = 2.075672141002979
y[1] (numeric) = 2.075671925386859
absolute error = 2.156161196253947e-07
relative error = 1.038777345256499e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.459
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.758
Order of pole (six term test) = -0.7175
TOP MAIN SOLVE Loop
x[1] = 2.470000000003079
y[1] (analytic) = 2.082862683349639
y[1] (numeric) = 2.082862463125308
absolute error = 2.202243303273121e-07
relative error = 1.05731564585501e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.469
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.776
Order of pole (six term test) = -0.7174
TOP MAIN SOLVE Loop
x[1] = 2.480000000003145
y[1] (analytic) = 2.090062438876704
y[1] (numeric) = 2.090062214047304
absolute error = 2.248293999862483e-07
relative error = 1.075706619114604e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.479
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.794
Order of pole (six term test) = -0.7173
TOP MAIN SOLVE Loop
x[1] = 2.49000000000321
y[1] (analytic) = 2.097271401315812
y[1] (numeric) = 2.097271171884475
absolute error = 2.294313370398982e-07
relative error = 1.093951583452455e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.489
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.812
Order of pole (six term test) = -0.7173
TOP MAIN SOLVE Loop
x[1] = 2.500000000003276
y[1] (analytic) = 2.104489564424695
y[1] (numeric) = 2.104489330394523
absolute error = 2.34030171686328e-07
relative error = 1.112051946669096e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.499
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.829
Order of pole (six term test) = -0.7172
TOP MAIN SOLVE Loop
x[1] = 2.510000000003341
y[1] (analytic) = 2.111716921987005
y[1] (numeric) = 2.111716683361099
absolute error = 2.386259061459839e-07
relative error = 1.130008968822632e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.509
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.847
Order of pole (six term test) = -0.7171
TOP MAIN SOLVE Loop
x[1] = 2.520000000003407
y[1] (analytic) = 2.118953467812185
y[1] (numeric) = 2.118953224593637
absolute error = 2.432185479683824e-07
relative error = 1.147823921869814e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.519
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.865
Order of pole (six term test) = -0.717
TOP MAIN SOLVE Loop
x[1] = 2.530000000003472
y[1] (analytic) = 2.126199195735325
y[1] (numeric) = 2.126198947927211
absolute error = 2.47808113140735e-07
relative error = 1.165498104024224e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.529
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.883
Order of pole (six term test) = -0.717
TOP MAIN SOLVE Loop
x[1] = 2.540000000003538
y[1] (analytic) = 2.133454099617008
y[1] (numeric) = 2.133453847222391
absolute error = 2.523946172061642e-07
relative error = 1.183032797619004e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.539
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.9
Order of pole (six term test) = -0.7169
TOP MAIN SOLVE Loop
x[1] = 2.550000000003603
y[1] (analytic) = 2.140718173343153
y[1] (numeric) = 2.140717916365093
absolute error = 2.569780597205806e-07
relative error = 1.200429196708592e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.549
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.918
Order of pole (six term test) = -0.7168
TOP MAIN SOLVE Loop
x[1] = 2.560000000003669
y[1] (analytic) = 2.147991410824913
y[1] (numeric) = 2.147991149266435
absolute error = 2.615584775433888e-07
relative error = 1.217688656599144e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.559
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.936
Order of pole (six term test) = -0.7168
TOP MAIN SOLVE Loop
x[1] = 2.570000000003734
y[1] (analytic) = 2.155273805998483
y[1] (numeric) = 2.155273539862617
absolute error = 2.661358662336966e-07
relative error = 1.234812326364272e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.569
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.954
Order of pole (six term test) = -0.7167
TOP MAIN SOLVE Loop
x[1] = 2.5800000000038
y[1] (analytic) = 2.162565352825006
y[1] (numeric) = 2.162565082114773
absolute error = 2.707102324528421e-07
relative error = 1.251801394576157e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.579
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.971
Order of pole (six term test) = -0.7166
TOP MAIN SOLVE Loop
x[1] = 2.590000000003865
y[1] (analytic) = 2.1698660452904
y[1] (numeric) = 2.169865770008793
absolute error = 2.752816068429809e-07
relative error = 1.268657147939928e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.589
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 7.989
Order of pole (six term test) = -0.7166
TOP MAIN SOLVE Loop
x[1] = 2.600000000003931
y[1] (analytic) = 2.177175877405229
y[1] (numeric) = 2.177175597555246
absolute error = 2.798499836309531e-07
relative error = 1.285380692185879e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.599
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.007
Order of pole (six term test) = -0.7165
TOP MAIN SOLVE Loop
x[1] = 2.610000000003996
y[1] (analytic) = 2.184494843204572
y[1] (numeric) = 2.184494558789194
absolute error = 2.844153779157921e-07
relative error = 1.301973217288833e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.609
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.025
Order of pole (six term test) = -0.7164
TOP MAIN SOLVE Loop
x[1] = 2.620000000004062
y[1] (analytic) = 2.191822936747897
y[1] (numeric) = 2.191822647770079
absolute error = 2.889778181192071e-07
relative error = 1.31843596156529e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.619
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.043
Order of pole (six term test) = -0.7164
TOP MAIN SOLVE Loop
x[1] = 2.630000000004127
y[1] (analytic) = 2.199160152118884
y[1] (numeric) = 2.199159858581585
absolute error = 2.935372984680384e-07
relative error = 1.33476999474193e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.629
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.06
Order of pole (six term test) = -0.7163
TOP MAIN SOLVE Loop
x[1] = 2.640000000004193
y[1] (analytic) = 2.206506483425343
y[1] (numeric) = 2.20650618533149
absolute error = 2.980938531571553e-07
relative error = 1.350976556816635e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.639
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.078
Order of pole (six term test) = -0.7162
TOP MAIN SOLVE Loop
x[1] = 2.650000000004258
y[1] (analytic) = 2.213861924799044
y[1] (numeric) = 2.213861622151577
absolute error = 3.026474675316138e-07
relative error = 1.367056653992031e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.649
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.096
Order of pole (six term test) = -0.7162
TOP MAIN SOLVE Loop
x[1] = 2.660000000004324
y[1] (analytic) = 2.221226470395601
y[1] (numeric) = 2.221226163197429
absolute error = 3.071981717894801e-07
relative error = 1.38301148434796e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.659
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.114
Order of pole (six term test) = -0.7161
TOP MAIN SOLVE Loop
x[1] = 2.670000000004389
y[1] (analytic) = 2.228600114394339
y[1] (numeric) = 2.228599802648367
absolute error = 3.117459721480031e-07
relative error = 1.398842125756264e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.669
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.131
Order of pole (six term test) = -0.716
TOP MAIN SOLVE Loop
x[1] = 2.680000000004455
y[1] (analytic) = 2.235982850998166
y[1] (numeric) = 2.23598253470728
absolute error = 3.162908859266622e-07
relative error = 1.414549694714638e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.679
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.149
Order of pole (six term test) = -0.716
TOP MAIN SOLVE Loop
x[1] = 2.69000000000452
y[1] (analytic) = 2.243374674433429
y[1] (numeric) = 2.24337435360051
absolute error = 3.208329193427062e-07
relative error = 1.4301352466847e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.689
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.167
Order of pole (six term test) = -0.7159
TOP MAIN SOLVE Loop
x[1] = 2.700000000004586
y[1] (analytic) = 2.250775578949797
y[1] (numeric) = 2.250775253577723
absolute error = 3.253720746165811e-07
relative error = 1.445599808615297e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.699
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.185
Order of pole (six term test) = -0.7158
TOP MAIN SOLVE Loop
x[1] = 2.710000000004651
y[1] (analytic) = 2.258185558820148
y[1] (numeric) = 2.258185228911776
absolute error = 3.299083721763907e-07
relative error = 1.460944477692792e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.709
Order of pole (three term test) = 1.508
Radius of convergence (six term test) for eq 1 = 8.203
Order of pole (six term test) = -0.7158
TOP MAIN SOLVE Loop
x[1] = 2.720000000004717
y[1] (analytic) = 2.265604608340427
y[1] (numeric) = 2.265604273898593
absolute error = 3.344418333384169e-07
relative error = 1.476170343700873e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.719
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.22
Order of pole (six term test) = -0.7157
TOP MAIN SOLVE Loop
x[1] = 2.730000000004782
y[1] (analytic) = 2.273032721829498
y[1] (numeric) = 2.273032382857054
absolute error = 3.389724438918051e-07
relative error = 1.491278328888183e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.729
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.238
Order of pole (six term test) = -0.7156
TOP MAIN SOLVE Loop
x[1] = 2.740000000004848
y[1] (analytic) = 2.280469893629073
y[1] (numeric) = 2.280469550128839
absolute error = 3.435002344787108e-07
relative error = 1.506269543125056e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.739
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.256
Order of pole (six term test) = -0.7156
TOP MAIN SOLVE Loop
x[1] = 2.750000000004913
y[1] (analytic) = 2.287916118103553
y[1] (numeric) = 2.287915770078329
absolute error = 3.480252237508807e-07
relative error = 1.521145032359656e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.749
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.274
Order of pole (six term test) = -0.7155
TOP MAIN SOLVE Loop
x[1] = 2.760000000004979
y[1] (analytic) = 2.295371389639897
y[1] (numeric) = 2.295371037092496
absolute error = 3.525474010501739e-07
relative error = 1.53590570415484e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.759
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.292
Order of pole (six term test) = -0.7154
TOP MAIN SOLVE Loop
x[1] = 2.770000000005044
y[1] (analytic) = 2.302835702647529
y[1] (numeric) = 2.302835345580736
absolute error = 3.570667934660321e-07
relative error = 1.550552621081559e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.769
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.309
Order of pole (six term test) = -0.7153
TOP MAIN SOLVE Loop
x[1] = 2.78000000000511
y[1] (analytic) = 2.31030905155821
y[1] (numeric) = 2.310308689974799
absolute error = 3.615834116565964e-07
relative error = 1.565086763663601e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.779
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.327
Order of pole (six term test) = -0.7153
TOP MAIN SOLVE Loop
x[1] = 2.790000000005175
y[1] (analytic) = 2.317791430825896
y[1] (numeric) = 2.317791064728632
absolute error = 3.660972640595617e-07
relative error = 1.579509092969209e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.789
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.345
Order of pole (six term test) = -0.7152
TOP MAIN SOLVE Loop
x[1] = 2.800000000005241
y[1] (analytic) = 2.325282834926636
y[1] (numeric) = 2.325282464318287
absolute error = 3.706083493426604e-07
relative error = 1.593820518416003e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.799
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.363
Order of pole (six term test) = -0.7151
TOP MAIN SOLVE Loop
x[1] = 2.810000000005306
y[1] (analytic) = 2.332783258358477
y[1] (numeric) = 2.332782883241778
absolute error = 3.751166990362265e-07
relative error = 1.608022081314948e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.809
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.381
Order of pole (six term test) = -0.7151
TOP MAIN SOLVE Loop
x[1] = 2.820000000005372
y[1] (analytic) = 2.340292695641288
y[1] (numeric) = 2.34029231601898
absolute error = 3.796223086993677e-07
relative error = 1.622114658591213e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.819
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.399
Order of pole (six term test) = -0.715
TOP MAIN SOLVE Loop
x[1] = 2.830000000005437
y[1] (analytic) = 2.347811141316706
y[1] (numeric) = 2.347810757191513
absolute error = 3.841251929870282e-07
relative error = 1.63609919991947e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.829
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.416
Order of pole (six term test) = -0.7149
TOP MAIN SOLVE Loop
x[1] = 2.840000000005503
y[1] (analytic) = 2.355338589947991
y[1] (numeric) = 2.355338201322621
absolute error = 3.886253701068654e-07
relative error = 1.649976660533749e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.839
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.434
Order of pole (six term test) = -0.7149
TOP MAIN SOLVE Loop
x[1] = 2.850000000005569
y[1] (analytic) = 2.362875036119895
y[1] (numeric) = 2.36287464299705
absolute error = 3.931228453879498e-07
relative error = 1.663747931560111e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.849
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.452
Order of pole (six term test) = -0.7148
TOP MAIN SOLVE Loop
x[1] = 2.860000000005634
y[1] (analytic) = 2.37042047443858
y[1] (numeric) = 2.370420076820956
absolute error = 3.976176237152629e-07
relative error = 1.677413893454646e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.859
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.47
Order of pole (six term test) = -0.7147
TOP MAIN SOLVE Loop
x[1] = 2.8700000000057
y[1] (analytic) = 2.377974899531502
y[1] (numeric) = 2.377974497421777
absolute error = 4.021097246287297e-07
relative error = 1.690975479631646e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.869
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.488
Order of pole (six term test) = -0.7147
TOP MAIN SOLVE Loop
x[1] = 2.880000000005765
y[1] (analytic) = 2.385538306047266
y[1] (numeric) = 2.385537899448106
absolute error = 4.065991605628483e-07
relative error = 1.704433584370169e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.879
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.505
Order of pole (six term test) = -0.7146
TOP MAIN SOLVE Loop
x[1] = 2.890000000005831
y[1] (analytic) = 2.393110688655558
y[1] (numeric) = 2.393110277569631
absolute error = 4.110859266326372e-07
relative error = 1.717789020714224e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.889
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.523
Order of pole (six term test) = -0.7145
TOP MAIN SOLVE Loop
x[1] = 2.900000000005896
y[1] (analytic) = 2.400692042047005
y[1] (numeric) = 2.400691626476958
absolute error = 4.155700477070923e-07
relative error = 1.731042717802101e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.899
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.541
Order of pole (six term test) = -0.7145
TOP MAIN SOLVE Loop
x[1] = 2.910000000005962
y[1] (analytic) = 2.408282360933079
y[1] (numeric) = 2.408281940881558
absolute error = 4.20051520677589e-07
relative error = 1.744195479282761e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.909
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.559
Order of pole (six term test) = -0.7144
TOP MAIN SOLVE Loop
x[1] = 2.920000000006027
y[1] (analytic) = 2.415881640045976
y[1] (numeric) = 2.415881215515612
absolute error = 4.24530363751785e-07
relative error = 1.757248189293354e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.919
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.577
Order of pole (six term test) = -0.7143
TOP MAIN SOLVE Loop
x[1] = 2.930000000006093
y[1] (analytic) = 2.423489874138529
y[1] (numeric) = 2.42348944513193
absolute error = 4.290065991341407e-07
relative error = 1.77020173969837e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.929
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.595
Order of pole (six term test) = -0.7143
TOP MAIN SOLVE Loop
x[1] = 2.940000000006158
y[1] (analytic) = 2.431107057984068
y[1] (numeric) = 2.431106624503847
absolute error = 4.334802210514965e-07
relative error = 1.78305689841133e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.939
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.612
Order of pole (six term test) = -0.7142
TOP MAIN SOLVE Loop
x[1] = 2.950000000006224
y[1] (analytic) = 2.438733186376368
y[1] (numeric) = 2.438732748425112
absolute error = 4.379512557051157e-07
relative error = 1.795814557130183e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.949
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.63
Order of pole (six term test) = -0.7141
TOP MAIN SOLVE Loop
x[1] = 2.960000000006289
y[1] (analytic) = 2.446368254129464
y[1] (numeric) = 2.44636781170977
absolute error = 4.424196933250357e-07
relative error = 1.808475451634202e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.959
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.648
Order of pole (six term test) = -0.7141
TOP MAIN SOLVE Loop
x[1] = 2.970000000006355
y[1] (analytic) = 2.454012256077617
y[1] (numeric) = 2.454011809192065
absolute error = 4.468855512307357e-07
relative error = 1.821040421146949e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.969
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.666
Order of pole (six term test) = -0.714
TOP MAIN SOLVE Loop
x[1] = 2.98000000000642
y[1] (analytic) = 2.461665187075182
y[1] (numeric) = 2.461664735726342
absolute error = 4.513488400803567e-07
relative error = 1.833510269593669e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.979
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.684
Order of pole (six term test) = -0.7139
TOP MAIN SOLVE Loop
x[1] = 2.990000000006486
y[1] (analytic) = 2.469327041996499
y[1] (numeric) = 2.469326586186932
absolute error = 4.558095669793261e-07
relative error = 1.845885778705097e-05 %
Correct digits = 7
h = 1e-05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.989
Order of pole (three term test) = 1.509
Radius of convergence (six term test) for eq 1 = 8.702
Order of pole (six term test) = -0.7139
Finished!
diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ;
Iterations = 100000
Total Elapsed Time = 3.0 Seconds
Elapsed Time(since restart) = 3.0 Seconds
Time to Timeout = 29 Minutes 57.0 Seconds
Percent Done = 100 %